> From: Gabriel Dos Reis <[EMAIL PROTECTED]>
>> Paul Schlie <[EMAIL PROTECTED]> writes:
> | > From: Gabriel Dos Reis <[EMAIL PROTECTED]>
> | > |Paul Schlie <[EMAIL PROTECTED]> writes:
> | > | Thank you. In essence, I've intentionally defined the question of x^y's
> | > | value about x=y->0 as a constrained "bivariate" function, to where only
> | > | the direction, not the relative rate of the argument's paths are
> | > | ambiguous, as I believe that when the numerical representation system
> | > | has no provision to express their relative rates of convergence, they
> | > | should be assumed to be equivalent;
> | >
> | > You're seriously mistaken. In lack of any further knowledge, one should
> | > not assume anything particular. Which is reflected in LIA-2's rationale.
> | > You just don't know anything about the rate of the arguments.
> |
> | I guess I'd simply contend that the value of a function about any point
> | in the absents of further formal constraints should be assumed to represent
> | it's static value about that point i.e. lim{|v|->1/inf) f(x+v, y+v, ...)
>
> That is menaingless.
>
> A floating point system is a projection on a discrete base set, as a
> consequence when you compute a value, you almost always don't get an
> element in that set: You need to make projection. Consistency predictable
- What is meaningless? lim{|v|->1/inf) f(x+v, y+v, ...) isn't meant to
necessarily be literally computed, but only abstractly express a limit
about a uniformly converging point, as a proposed generally useful and
predictable basis of a functions value definition; as opposed to assuming
that if a function's arguments about some point are subject to some very
specific but non-specifiable set of constraints which yield an ambiguity,
it's value is deemed generally ambiguous, and appropriate to return a Nan
result for the remaining infinite-1 set of conditions where it's otherwise
reasonably well defined at that limit (which seems counterproductive).
> | And reserve the obligation for applications requiring the calculation
> | of formally parameterized multi-variate functions at boundary limits to
> | themselves; rather than burdening either uses of such functions with
> | arguably less useful Nan results.
>
> But that is nnot
- We simply disagree. As I perceive Nan run-time results to be about as
useful as an "I don't know" response to a question which demands an
answer, even if only the most typically useful one. (Where if a more
accurate situation specific results are required, I perceive it as the
application's responsibility to provision, thereby not burdening either
with run-time "I don't know" responses.
> | But understand, that regardless of my own opinion; it's likely more
> | important that a function produces predicable results, regardless of
> | their usefulness on occasion. (which is the obligation of the committees
> | to hopefully decide well)
